Search for maximum points of a vector criterion based on decomposition properties

We address the problem of optimal reconstruction of the values of a linear operator on ℝ ^d or ℤ ^d from approximate values of other operators. Each operator acts as the multiplication of the Fourier transform by a certain function. As an application, we present explicit expressions for optimal methods of reconstructing the solution of the heat equation (for continuous and difference models) at a given instant of time from inaccurate measurements of this solution at other time instants.     

Effect of Two Different UVA Doses on the Rabbit Cornea and Lens

The aim of the present paper was to examine the irradiation effect of two doses of UVA rays (365 nm) on the rabbit cornea and lens. Corneas of anesthetized adult albino rabbits were irradiated with UVA rays for 5 days (daily dose 1.01 J cm⁻² in one group of rabbits and daily dose 2.02 J cm⁻² in the second group of animals). The third day after the last irradiation, the rabbits were killed, and their eyes were employed for spectrophotometrical, biochemical and immunohistochemical investigations. Normal eyes served as controls. Absorption spectra of the whole corneal centers were recorded over the UV–VIS (visible) spectral range. Levels of antioxidant and prooxidant enzymes, nitric oxide synthases and nitric oxide (indirectly measured as nitrate concentration) were investigated in the cornea. Malondialdehyde, a byproduct of lipid peroxidation, was examined in the cornea and lens. The results show that the staining for endothelial nitric oxide synthase was more pronounced in corneas irradiated with the higher UVA dose. Otherwise, UVA rays at either dose did not significantly change corneal light absorption properties and did not cause statistically significant metabolic changes in the cornea or lens. In conclusion, UVA rays at the employed doses did not evoke harmful effects in the cornea or lens.     

Functional Representations of Lawson Monads

We introduce a class of Lawson monads and show that these monads have a functional representation. A characterisation of such a representation for the inclusion hyperspace monad is given.     

Large free sets in powers of universal algebras

We prove that for each universal algebra ${(A, \mathcal{A})}$ of cardinality ${|A| \geq 2}$ and infinite set X of cardinality ${|X| \geq | \mathcal{A}|}$ , the X-th power ${(A^{X}, \mathcal{A}^{X})}$ of the algebra ${(A, \mathcal{A})}$ contains a free subset ${\mathcal{F} \subset A^{X}}$ of cardinality ${|\mathcal{F}| = 2^{|X|}}$ . This generalizes the classical Fichtenholtz–Kantorovitch–Hausdorff result on the existence of an independent family ${\mathcal{I} \subset \mathcal{P}(X)}$ of cardinality ${|\mathcal{I}| = |\mathcal{P}(X)|}$ in the Boolean algebra ${\mathcal{P}(X)}$ of subsets of an infinite set X.     

Origin of large Landau-Placzek ratio in a liquid metallic alloy

Dynamic structure factors for Na(c)K(1-c) liquid metallic alloys and pure components are studied by molecular dynamics simulations. Large values of Landau-Placzek ratio for four compositions of the liquid alloy are analyzed by wave-number dependent contributions from relaxation and propagating processes within the generalized collective modes method. The origin of the large Landau-Placzek ratio for liquid alloys is discussed.     

Characterizing compact Clifford semigroups that embed into convolution and functor-semigroups

We study algebraic and topological properties of the convolution semigroup of probability measures on a topological groups and show that a compact Clifford topological semigroup S embeds into the convolution semigroup P(G) over some topological group G if and only if S embeds into the semigroup exp(G)\exp(G) of compact subsets of G if and only if S is an inverse semigroup and has zero-dimensional maximal semilattice. We also show that such a Clifford semigroup S embeds into the functor-semigroup F(G) over a suitable compact topological group G for each weakly normal monadic functor F in the category of compacta such that F(G) contains a G-invariant element (which is an analogue of the Haar measure on G).     

Convexities Generated by <Emphasis Type="Italic">L</Emphasis>-Monads

Let \mathbbF\mathbb{F} be a monad in the category Comp. We build for each \mathbbF\mathbb{F}-algebra a convexity in general sense (see van de Vel 1993). We investigate properties of such convexities and apply them to prove that the multiplication map of the order-preserving functional monad is soft.     

Average g-factors for high-spin states in 78Kr

Inverse reactions of ^{63, 65}Cu beams on ^{18, 16}O targets have been used to populate states of ⁷⁸Kr by fusion-evaporation reactions. The excited nuclei recoiled at high velocity v/c ≈ 7 % through a polarized iron (⁵⁴Fe) layer and were stopped in a copper layer. During the period in iron, 0.05–0.65 ps, the nuclei were subjected to the intense transient magnetic field (initially ～ 3500 T). The resulting precession of the high-spin nuclear states populated during this time was determined by measuring the time integral rotation angle of the discrete γ-ray transitions at low spin.The average g-factor at low spin 2 ≦ J ≦ 8 compared to that at higher spin 8 ≦ J ≦ 12 in ⁷⁸Kr was found to be identical within the experimental uncertainties of ～ 15 %. This result implies that either there are no rotational alignment effects at the backbend in ⁷⁸Kr or more plausibly, proton (g ≈ 1) and neutron (g ≈ 0) aligned bands are equally competitive and both populated in the reaction. It is then likely that the resulting g-factor represents an average over many populated proton and neutron aligned bands.     

Nuclear spectroscopy in 48V via the 34S(16O,pn)48V reaction

The electromagnetic decays of 18 bound states in ⁴⁸V have been studied via the ³⁴S(¹⁶O, pn)⁴⁸V reaction, at incident ion energies of 30–36 MeV. At these energies pn, 2pn, 2p, αp, αn and 2n exit channels were open. Spins and parities of the levels as well as the branching and mixing ratios of their decay γ-rays have been obtained from angular distribution, excitation function, and high resolution γ-γ and n-γ coincidence measurements. Six, and possibly seven, members of a very pure rotational negative parity band have been identified. This band is based on a 1^? low-lying core excited state with probable configuration $\text{(π}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}\text{(π}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{)}{}^4\text{(ν}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{)}{}^5$.